Optimal regularity of mixed Dirichlet-conormal boundary value problems for parabolic operators

2021/01/05 by Jongkeun Choi, Hongjie Dong, Choi, Jongkeun +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2101.01654

openalex publication_date 2021/01/05 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28

Abstract

We obtain the regularity of solutions in Sobolev spaces for the mixed Dirichlet-conormal problem for parabolic operators in cylindrical domains with time-dependent separations, which is the first of its kind. Assuming the boundary of the domain to be Reifenberg-flat and the separation to be locally sufficiently close to a Lipschitz function of m variables, where m=0,…,d-2, with respect to the Hausdorff distance, we prove the unique solvability for p∈ (2(m+2/(m+3),2(m+2)/(m+1))). In the case when m=0, the range p∈(4/3,4) is optimal in view of the known results for Laplace equations.

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